The resulting transformation is a rotation by 2q about the point of
intersection of the lines. If the direction of the angle q is from
the first line of reflection to the second, then the direction of rotation
is the same as the direction of q.
Youshould probably check that the same thing works if you reflect in
the further line first (remembering that this means the direction is reversed),
and if the flag is between the two lines.
We just need to check the result for a single point, because then every
point will rotate by the same amount and so the flag will remain intact
(and will have rotated by the same amount).
The diagram says it all, really: the line segment joining the point to the
origin has rotated by an angle of a+a+(q-a)+(q -a)=2q in the direction of q.
